电子电工技术英文课件 (58).pdf

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1、6.2 Filters 6.2.1 Definition of Filter A filter shown in Fig.1 is a combination of passive(R,L and C)and/or active(transistors of operational amplifiers)elements,which is designed to pass or reject signals with a band of frequencies.Filters are widely applied in communication system,stereo system,po

2、wer system,and so on.FilterInputOutput Figure 1:Filter.To understand filters in detail,it is essential to learn the concept of transfer function.6.2.2 Transfer Function and Filter Types A transfer function is the frequency-dependent ratio of an output to an output,as shown in Fig.2.The transfer func

3、tion of the circuit is defined as ()()=HYX(1)where H()is the transfer function,X()is the input phasor of voltage or current,Y()is the output phasor of voltage or current.LinearCircuitH()InputOutput()X()Y Figure 2:Transfer function.The transfer function H()can reveal the frequency characteristics of

4、a circuit.According to the frequency characteristics of the magnitude of the transfer function,there are four types of filters:(1)Lowpass filter as shown in Fig.3(a)(2)Highpass filter as shown in Fig.3(b)(3)Bandpass filter as shown in Fig.3(c)(4)Bandstop filter as shown in Fig.3(d)StopbandPassband()

5、H StopbandPassband()H(a)(b)StopbandPassband()HStopband StopbandPassband()HPassband(c)(d)Figure 3:Filter types:(a)lowpass filter;(b)highpass filter;(c)bandpass filter;(d)bandstop filter.6.2.3 Lowpass Filter and Highpass Filter A lowpass filter is designed to only allow low-frequency signals to pass t

6、hrough but blocks the transmission of high-frequency signals.The series RC circuit shown in Fig.4 is a typical lowpass filter when the capacitor voltage is the output signal.InputOutputiVRoV1j CLowpass filter Figure 4:RC lowpass filter.The transfer function of the circuit in Fig.4 is oi(11()1)1j CjR

7、 CRj C=+VHV(2)According to(2),the plot of()H is displayed in Fig.5.c0.707PassbandPassbandStopbandStopband()H Figure 5:Frequency characteristics of a RC lowpass filter.cin Fig.5 is known as the cutoff frequency,and is obtained by setting 2()0.7072=H.From(2),it is obvious that c1RC=(3)A highpass filte

8、r is designed to only allow high-frequency signals to pass through but blocks the transmission of low-frequency signals.If the positions of the resistor and capacitor are interchanged and the resistor voltage is the output signal,the series RC circuit in Fig.6 is a typical highpass filter.InputOutpu

9、tiVRoV1j CHighpass filter Figure 6:RC highpass filter.The transfer function of the circuit in Fig.6 is oi(11()1)1RRjj CR C=+VVH(4)According to(4),the plot of()H is displayed in Fig.7.c0.707PassbandPassbandStopbandStopband()H Figure 7:Frequency characteristics of a RC highpass filter.We can also appl

10、y series RL circuit to form a lowpass filter and a highpass filter,as shown in Fig.8.You can derive the transfer functions and plot()H by yourself.iVRoVj LLowpass filter iVRoVj LHighpass filter Figure 8:RL filters.6.2.4 Bandpass Filter and Bandstop Filter A bandpass filter is designed to only allow

11、signals within a band of frequencies,c1c2 to pass through but blocks the transmission of signals outside the band of frequencies.The series RLC circuit shown in Fig.9 is a typical lowpass filter when the resistor voltage is the output signal.InputOutputiVRoV1j CBandpass filterj L Figure 9:RLC bandpa

12、ss filter.The transfer function of the circuit in Fig.9 is oi(111)()(1RRj LjLj CC=+VVH(5)The plot of()H is displayed in Fig.10.c2c1 is known as bandwidth.c10.707PassbandPassbandStopbandStopband()HStopbandStopbandc2 Figure 10:Frequency characteristics of a RLC bandpass filter.If the positions of LC a

13、nd R and the LC voltage is the output signal,the series RLC circuit in Fig.11 is typical bandstop filter.InputOutputiVRoV1j CBandstop filterj L Figure 11:RLC bandstop filter.The transfer function of the circuit in Fig.11 is oi()()111)1(j LjLj CCRj LRjLj CC+=+HVV(6)The plot of()H is displayed in Fig.

14、12.c10.707PassbandPassbandStopbandStopband()Hc2PassbandPassband Figure 12:Frequency characteristics of a RLC bandstop filter.6.2.5 Active Filter All filters introduced above are passive filters because resistors,capacitors,and inductors are all passive elements.In contrast,active filters contain bot

15、h passive elements and active elements such as operational amplifiers and transistors.One advantage of the active filters is that they can achieve signal amplification.A typical lowpass active filter is shown in Fig.13.The transfer function of the circuit in Fig.12 is ifff1fo1()111()()1R jCRjRCRRjRC

16、+=+HVV(7)The transfer function of the circuit in Fig.12 is ifff1fo1()111()()1R jCRjRCRRjRC+=+HVV(8)From(8),the transfer function satisfies the frequency characteristics of the lowpass filter.InputOutputiVfRoV1j C1R Figure 13:Lowpass active filter.此处绘制电容电阻串联电路 滤波器首先以 RC 为例，从极端情况开始分析（频率足够高，足够低，开路、短路）然

17、后给出一般情况，说明 0.707 是分界点 然后对 RL 做类似分析 最后给出 RLC 串联带通滤波器，说明带宽等术语 用传递函数进一步升华对滤波器的理解，给出带阻滤波器的分析。给一个含运放的滤波器。谐振。首先从带通滤波器讲起，说明谐振峰所对应的是谐振角频率。然后说明谐振的广泛用途。再给出串联谐振的特点分析。强调谐振最大功率，品质因数，频率选择性 给出收音机电路分析 三相 首先给出三相发电机、三相电压时域形式（既体现最大值，又体现有效值）和波形，三相相量形式（有效值相量），说明三相的好处，强调三相的平衡 其次出三相化为单相 再给出三相连接方式，并给出线电压、线电流等定义 最后给出三相功率测量

18、给出不平衡三相 三相可以考虑加入三相变压器。（Ulaby 教材）In this circuit if we consider the current of the resistor,the high frequency component is easy to flow into the resistor through the capacitor,while the low frequency component is blocked by the capacitor and difficult to flow into the resistor.The capacitor has the

19、characteristic of passing high frequency and rejecting low frequency.So we call the capacitor in this circuit as a high-pass filter.另起一页（上一页电路图重现）If we replace the capacitor with an inductor,此处抹去电容，换成电感。the low frequency component is easy to flow into the resistor through the inductor,while the high

20、 frequency component is blocked by the inductor and difficult to flow into the resistor.The inductor has the characteristic of passing low frequency and rejecting high frequency.Therefore,we call the inductor in this circuit as a low-pass filter.另起一页：If the inductor and capacitor are connected in se

21、ries between the voltage source and resistor,此处绘制 RLC 串联电路 only some components within a region between high frequency and low frequency are easy to pass for the inductor rejects high frequency and the capacitor rejects low frequency.So the inductor and capacitor in series in this circuit is a band-pass filter.